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The problem of nonlinear dynamics of an of elastic rod system connected to a spacecraft in a reduced quasi-static bending statement

Russkikh S.V.

#### Abstract:

Nonlinear dynamics of a planar rod system consisting of elastic inextensible rods, connected at the ends by elastic knot joints that allow large angles of rotation, is considered. The rod system is connected to an undeformed spacecraft that makes a turn about its center of gravity and movements along the horizontal and vertical axis as a free solid body. The motion of the system under consideration is described in a mobile coordinate system. The displacements of each rod are characterized by its final rotation as a rigid body with respect to a straight line passing through two adjacent hinges and a bend with a small transverse displacement. The equations of motion in compact form with the necessary explanations are given, which are obtained at speeds for the spacecraft and in the selected generalized coordinates for the rod system on the basis of the principle of possible displacements. Equations are also obtained in a matrix form convenient for numerical integration. The statement of the problem is presented, which is obtained by reducing the initial system of equations by quasistatic bending. From the equations of motion, “rapid” movements are excluded, which represent the bending of each rod, i.e. the first and second derivatives of the angles between the tangent to the curved axis of the rod and its undeformed axis. As a result, a new system of equations with necessary explanations is written in the matrix form. Examples of calculations with the necessary comparisons between two approaches are given: the problem of the reaction of a rod system to an arbitrary perturbing impulse; the problem of the deployment of the rod system from one position to another by the inclusion of elastic-viscous clamps integrated into the hinges, due to centrifugal and inertial forces.

#### Keywords:

mobile coordinate system,

nonlinear dynamics,

quasi-static bend,

reduction,

rod system,

spacecraft,

transformable system,

квазистатический изгиб,

космический аппарат,

нелинейная динамика,

подвижная система координат,

редуцирование,

стержневая система,

трансформируемая система
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